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No, you’ll have a few minor manual steps to take. The adapter plugs into your computer and will appear at a serial port (e.g. /dev/ttyAMA0 on Linux or COM1 on Windows). You’ll have to configure openHAB by creating a Thingand telling it what the path to that serial port it. And then the devices need to be paired with the coordinator. You’ll have to read the manual of the device to see how this is done. Typically you will scan for new Zigbee devices from the openHAB inbox and then you’ll need to perform some operation on the device (e.g. press a button).
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It’s hard to say. I don’t know that there are many people on this forum who have experience with all three and you will have a negative bias against HomeAssistant as those users here that do have experience with it have left it for one reason or another. For the most part the decision on which one to use is driven by what devices are supported. Each has their own strengths and weaknesses in that respect. What I can say about Mozilla Things though is it’s more a standard unto itself and less a hub that works with lots of different standards like HA and OH. Their audience is people who want to build their own IoT devices whereas OH and HA’s audience are those who want to integrate IoT devices that use multiple different technologies and standards.
For OH 2.5 see How to get started (there is no step-by-step tutorial) .
For OH 3 see [wiki] Getting Started with OH3: rewriting the tutorial - 1. Introduction which is currently being moved to the official docs.